How to multiply square roots?
Answer: To multiply square roots, we multiply the whole number part and the square root parts separately.
Let's understand the solution in detail.
Let's understand this with some examples:
Example 1: Multiply √15 by √11.
In this case, both of them are under the square root sign. Hence, we can multiply them directly.
⇒ √15 × √11 = √165
Example 2: Multiply √3 by 4.
In this case, one of them is under the square root sign and the other is a whole number. Hence, we can multiply them directly.
⇒ √3 × 4 = 4√3
In this case, first, we convert 4 in such a way that it's under the square root sign.
Here, 4 = √16.
Now, we multiply them.
⇒ √3 × √16 = √48 = 4√3
Note that we could directly write it as 4√3, but it's always better to follow every step while learning.
Example 3: Multiply 3√5 by 3√6.
Here, first, we convert 3√5 and 3√6 to suitable forms.
Hence, 3√5 = √(5 × 9) = √45.
And 3√6 = √(6 × 9) = √54.
Now, multiplying both the numbers under the square root, we get √2430.
We can write √2430 = 9√30.
Another method is to multiply the whole number part and the radical part separately to give the answer. It is a lot easier way.
Note that we could also simply multiply as 3√5 × 3√6 = 9√30.
Hence, to multiply square roots, we multiply the whole number part and the square root part separately.